ABSORPTION SYSTEM DIVERSIFICATION INFLUENCE ON TEWI

Transcription

1 ABSORPTION SYSTEM DIVERSIFICATION INFLUENCE ON TEWI Dr ROBERT TOZER MSc PhD CEng MCIBSE MInstR MASHRAE Watrman Gor, Mchanical and Elctrical Consulting Enginrs, London, England ZAFER URE MSc MCIBSE MASHRAE MInstR Environmntal Procss Systms Ltd, Brkshir, England Modrn rfrigration tchnology including absorption rfrigration has coxistd with th mor standard typ of vapour comprssion systms vr sinc th bginning of rfrigration. Absorption rfrigration mainly rquirs a hat sourc to driv its cooling cycl. Only in th USA and Japan is absorption rfrigration widsprad in th markt, a markt tndncy of th last dcads. Concrns rgarding th Global Warming Potntial and th mor rcntly dfind Thrmal Equivalnt Warming Impact (TEWI) is an opportunity to furthr xplor th applications of absorption rfrigration. TEWI considrs both th dirct rfrigrant ffct and th primary nrgy impact on th quivalnt carbon dioxid (CO 2 ) missions. This papr xplors ths applications ovr a rang of annual oprating tims, and thrfor maks rcommndations on absorption systm divrsification to rduc th TEWI. List of symbols B Thrmal xrgy (kw) c p Spcific hat (kj/kgk) COP Cofficint of prformanc CO2 Equivalnt missions (kg CO 2 /kwh) flh Equivalnt full load hours (hours) E Enrgy (kwh or GJ) f Factor F Exrgy of Ful (kw) h Enthalpy (kj/kg) HDR Hat Dissipation Ratio I Indirct missions (ton CO 2 / lif) k Spcific xrgy consumption (kw/kw) k* Spcific xrgtic cost ( / ) l Rfrigrant lakag and purg (%) L Lakag & rlas (ton CO 2 /lif) m Mass flow rat (kg/s) n Numbr of yars (yars) N Numbr of stags poh Plant on hours (hours) p Prssur (kpa) P Exrgy of Product (kw) Q Hat (kw) R Rcovry losss (ton CO 2 / lif) s Entropy (kj/kgk) s Rfrigrant rlas (%) t Tmpratur ( C) T Absolut tmpratur (K) W Work or Elctric Powr (kw) α Rfrigrant rcovry factor α Thrmodynamic ratio Diffrnc ε Utilisation factor η Efficincy φ Dstroyd xrgy (kw) 1

2 Subscripts burn burnr ch chillr chp combind hat & powr / cognration comp comprssor ct cooling towr cw condnsr watr vaporator flh quivalnt full load hours g gnrator (of absorption chillr) g grid (lctric) hw hot watr m motor ng natural gas p pump poh plant on hours q thrmal r rfrigrant s ntropy w lctricity 0 rfrnc stat Suprscripts b xrgy nrgy 1. Introduction Any chang in rfrigration tchnology by mans of introducing nw rfrigrants or by adopting nw tchniqus must b carfully balancd to rduc th ovrall nvironmntal impact (Ur 1995, 1996a, 1996b). This has rcntly bn classifid as Total Equivalnt Warming Impact (TEWI), in which th influnc upon th Grnhous Effct rfrrd to as Global Warming Potntial (GWP), can b judgd for th opration of individual rfrigration plants (BRA 1996). TEWI calculations ar basd on two catgoris, namly Dirct GWP and Indirct GWP. Th Dirct GWP is producd mainly by all halognatd rfrigrants, including HFCs such a HFC 134a which is usd in this papr as th bas cas with cntrifugal chillrs. Th Indirct GWP is attributd to th indirct CO 2 mission du to th nrgy usag for th duration of its usful lif. Th amount of CO 2 missions havily dpnds on th typ of lctricity gnration and powr plant tchnology which varis from on country to anothr (Bggs 1994). Rfrigration with absorption chillrs is possibl at vaporating tmpraturs ranging from 10 C to as low as -50 C with a varity of cycls and fluids. Absorption systms, which ar hat drivn, can both cool and hat for human comfort and procss applications. Practically any typ of hat sourc can b usd to driv th absorption cycls, but this papr will only concntrat on th options mostly applid to th markt, which ar dirct fird on natural gas, and indirctly hat drivn via cognration systms (Tozr and Jams 1995). In addition to this th absorption chillrs considrd us th binary mixtur watr and lithium bromid whr watr is th rfrigrant. By doing so, th dirct rfrigrant impact on TEWI is liminatd from ths absorption options. Singl and doubl stag units ar usd whrby th cofficint of prformanc (COP) is rlatd to th numbr of stags and is dfind as th ratio of cooling output with rspct to hating input. To allocat TEWI valus to lctricity and hat producd by cognration systms, it has bn ncssary to rfr to thrmoconomic tchniqus (Lozano & Valro 1993). Th thrmodynamic componnt of such an analysis can convnintly b basd on scond law availability (Moran 1989) or xrgy (Kotas 1995) concpt, which is a masur of th usfulnss of nrgy. 2

3 Th rsults obtaind by applying th thory to slct absorption chillrs basd on TEWI calculations ar prsntd. For compltnss th appndics giv a brif introduction to th concpt of xrgy and TEWI allocations. 2. Allocation of variabls using xrgy Svral thoris hav bn dscribd (Lozano t al 1994) rgarding how th nrgy costs ar to b allocatd to th thrmal and lctric nrgy producd by th sam Cognration plant, which consums a ful, i.. natural gas. Th main concpt is that variabls such as costs or TEWI valus should b allocatd in accordanc with th usfulnss of th nrgy producd by a cognration plant. Exrgy is th thrmodynamic variabl that bst quantifis th usfulnss of nrgy. 2.1 Exrgy An introduction to th thortical concpt of xrgy is dtaild in Appndix A. Howvr, xrgy is not a wid sprad concpt and a coupl of practical xampls ar givn to provid an indicativ guid of its us in practical situations. Th usfulnss of thrmal nrgy dpnds strongly on its tmpratur. Dpnding on th fluid, tmpratur will dtrmin its prssur. For xampl, if only tmpratur is considrd, th sam amount of nrgy at diffrnt tmpraturs can b usd in diffrnt ways. At 2000 C it can driv powr stations with high fficincis (0.45), at 800 C th fficincy is 0.15 at 400 C th fficincy drops to blow 0.1. With lowr tmpratur applications, hat sourcs at 80 C can b usd for dirct or radiant hating. At 30 C hating is limitd to fabric radiant hating and at 20 C no hating is possibl bcaus it is qual to th rfrnc tmpratur. Howvr, in Antarctica, which has a lowr rfrnc tmpratur, a hat sourc at 20 C could by usful. Th sam concpt applis to absorption chillrs whr th following approximat valus ar givn (Tozr 1995, Tozr & Jams 1995b). Singl stag chillrs hav a COP of 0.7 and rquir a hat sourc of 100 C. Doubl stag chillrs hav a COP of 1.1 but rquir a highr tmpratur hat sourc of 160 C. Tripl stag chillr whn thy bcom availabl on th markt with hav COPs around 1.6 but will rquir highr tmpratur hat sourcs around 200 C or mor. Again th concpt of xrgy is applid whrby mor cooling can b achivd with mor stags and highr tmpratur hat sourcs. 2.2 TEWI Allocation Th TEWI allocation was basd on th spcific xrgy (not, not nrgy) costs of both thrmal and lctric nrgis bing idntical. This ncssarily implis that th TEWI allocations of thrmal nrgy will b lowr than lctric nrgy. Th invrs of th xrgtic fficincy (η) is th spcific xrgy consumption; th ratio of th xrgy of th thrmal and lctric products (P) with rspct to th xrgy of th natural gas ful (F) (Lozano & Valro 1993). P η b [1] F 3

4 F k 1 [2] P η b Appndix B givs dtails of th TEWI allocation calculations using Exrgy. Th TEWI allocations for lctric and thrmal nrgy producd by a cognration plant ar dtaild blow, in trms of th xrgy fficincy, th Carnot factor and th missions of natural gas supplying th cognration plant. T0 fcarnot 1 [3] T CO2wchp [4] b η fcarnot CO2qchp [5] b η 3. Plant Dsign Th spradsht dtaild in Tabl 1 provids information on diffrnt typs of absorption chillrs in ordr to dtrmin in subsqunt tabls thir TEWI basd on xrgy fficincy allocatd to ach cas. Th objctiv is to dtrmin th chillr with th lowst TEWI basd on only th chillr itslf. Th following chillrs ar considrd (Tozr t al 1995): Typ of Chillr Symbol a) Singl stag absorption chillr, hot watr 85 C A1,w85 b) Singl stag absorption chillr, hot watr 100 C A1,w100 c) Singl stag absorption chillr, hot watr 115 C A1,w115 d) Doubl stag absorption chillr, dirct fird drivn A2,df ) Doubl stag absorption chillr, stam drivn A2,st f) Doubl stag absorption chillr, xhaust gas drivn A2,hr g) Cntrifugal comprssor chillr, lctric drivn Cntrif Tabl 1 provids dsign dtails of all th rlatd plant itms that vary in trms of th typ of chillr, i..: hot watr pumps, condnsr watr pumps and cooling towr. Th Hat Dissipation Ratio (HDR) is th ratio of condnsr and absorbr hat (if applicabl) with rspct to th vaporator hat (Tozr 1991, 1992). It is important bcaus of th nrgy rquirmnts to dissipat this hat through dry coolrs of cooling towrs. In th cas of dirct fird chillrs th fficincy of th burnr has also to b takn into account. ηburn HDR 1+ [6] COP Th Carnot factor indicats th quality of nrgy and is usd for xrgy costing, quation [3]. Th main nrgy input to th chillrs dpnds on th chillr capacity (vaporator hat) and COP. For absorbr chillrs th main hat input is to th gnrator (Q ), whras for cntrifugal chillrs, this is to th comprssor. Q Qinput [7] COP Th xrgy input rsults from applying th Carnot factor to th nrgy input. T0 Binput fcarnotqinput 1 T Q input [8] 4

5 Th mass flow rat of condnsr watr is calculatd in trms of th chillr capacity, Hat Dissipation Ratio and condnsr watr diffrntial. Q HDR mcw [9] cp tcw Th condnsr watr pump powr is dpndnt on th flow rat, prssur drop and pump and motor fficincis. mcw pcw Wcw [10] ηη p m Th cooling towrs wr slctd for ach cas although a spcific powr rquirmnt pr hat dissipatd could hav bn assumd. Th total lctric powr of all plant is: W Wch + Whw + Wcw + Wct [11] For nrgy costs it is important to dtrmin th hours of opration of ach plant. For comprssor powr of cntrifugal chillrs and gnrator input to absorbr chillrs, Equivalnt Full Load Hours (EFLH) wr usd. For all othr lctric quipmnt Plant On Hours (POH) wr usd. Thrfor it was ncssary to dtrmin th powr corrsponding to both of ths running hours. DESIGN Symbol a) b) c) d) ) f) g) Chillr Typ Absorp Absorp Absorp Absorp Absorp Absorp Cntrif Capacity kw Q Stags N Enrgy Sourc hw85 hw100 hw115 dirct fird stam hat rcov lctric Tmp. of hat sourc C t input N/A. Cofficint of prformanc COP Burnr fficincy η burn 0.88 Hat dissipation ratio HDR Rfrnc tmpratur C t Carnot factor f carnot Enrgy input kw Q input Absorption Th nrgy kw Q g Exrgy input kw B input Auxiliary chillr powr kw W ch Cntrifugal comprssor kw Wcomp 382 Hot watr pump kw W hw Cond watr tmp. diff K t cw Condnsr watr flow l/s m cw Cond watr prss drop kpa p cw Cond watr pump ffic. η p Cond. wtr pump motor ff. η m Cond wtr pump powr kw W cw Cooling towr fan kw W ct ELECT POWER kw W Elctric flh kw W flh

6 Elctric poh kw W poh Tabl 1: Plant Dsign Dtails A prliminary analysis of this tabl indicats th following: - Th xrgy input to singl and doubl stag absorption chillrs is approximatly qual (xcluding dirct fird). In thory both singl and doubl stag chillrs ar quivalnt, i.. singl stag chillrs hav lowr COPs but rquir lowr grad nrgy than doubl stag chillrs (Tozr 1995). - Hat Dissipation Ratio: In practical applications this is th prdominant factor in nrgy usag, whr doubl stag absorption chillr bnfits from lowr Hat Dissipation Ratios than singl stag chillrs (Tozr & Jams 1995). 4. Enrgy In Tabl 2 th nrgy is valuatd for a rang of Equivalnt Full Load Hours (flh) and Plant On (running) Hours (poh). It was assumd that th plant on hours was 50% highr than th quivalnt full load hours. Th tabl indicats th typ Cognration systm, i.. ngin or turbin, and thrfor spcific Cognration systm costs ar indicatd in trms of th lctric output capacity. Th quivalnt full load hours of Cognration annual opration is assumd at 5000 hours. Th lctric and thrmal nrgis togthr with th total xrgtic prformancs ar indicatd for ach cas. ENERGY Symbol a) b) c) d) ) f) g) Equivalnt full load hours flh Plant on hours poh Numbr of yars n Cognration systm ngin ngin ngin non turbin turbin non Cognration lc. prform. η w Cognration xrgy prf. η b Elctric nrgy kwh E Thrmal nrgy MWh Eq Tabl 2: Enrgy Calculations Th lctric nrgy is basd on both flh and poh plants. Ew flh Wflh + poh Wpoh [12] Thrmal nrgy is drivd basd on th quivalnt full load hours of hat rquird to run th absorption chillrs. Eq flh Qg [13] 5. TEWI Calculations 6

7 Tabl 3 provids th dtaild calculations of TEWI for ach cas. Th Cognration lctric and thrmal TEWI allocations ar basd on th lctric and thrmal prformanc amongst othrs. Rfr to Appndix B for furthr dtails. Thrmal and lctric nrgy TEWI valus ar allocatd to ach cas dpnding on whthr it is supplid via a Cognration systm or through th lctric or natural gas grids. Th Carbon Dioxid (CO 2 ) missions for natural gas and grid lctricity ar 0.18 and 0.53 kg CO 2 /kwh rspctivly. (BRA 1996). TEWI Symbol a) b) c) d) ) f) g) Global Warming Potntial GWP 1300 Rfrigrant charg m r 450 Annual lakag % l1 2 Annual purg % l2 0.5 Annual srvic rlas % s Annual accidntal rlas % s2 0 Lakag CO 2 ton/lif L 161 Rfrigrant rcovry factor α 0.95 Rcovry losss ton/lif R 29 CO2 missions/kwh grid Cg CO2 missions/kwh cogn Cchp Elctric Enrgy kwh E CO2 miss / kwh nat gas Cng CO2 miss/kwh Cogn hat Cqchp Indirct ton CO 2 / lif I TEWI ton CO 2 / lif TEWI Tabl 3: TEWI Calculations Th TEWI valus wr stablishd for various Equivalnt Full Load Hours and th rsults ar rprsntd in Figur 1. Figur 1 indicats th following: - Doubl stag stam drivn absorption chillr. This option rsultd in th bst ovrall TEWI valus for all EFLH and approximatly 25% lowr than thos of th quivalnt cntrifugal chillr. This unit has an xcllnt COP du to that it uss th stam condnsat hat to improv fficincy. - Doubl stag hat rcovry drivn absorption chillr. Abov 900 EFLH it rsultd in marginally lowr TEWI valus. Du to th high initial costs of ths units, it can not b rcommndd as a viabl proposal (Tozr t al 1995). - Singl stag hot watr drivn absorption chillrs. Within this group th bst rsults wr obtaind for low hot watr tmpraturs, i.. 85 C as opposd to 100 C and 115 C. This is mainly du to th influnc of tmpratur on th xrgy allocation of TEWI valus. This option is th most favourabl in conomic trms (Tozr & Jams 1996), but from th TEWI standpoint can only b rcommndd for low running hour applications blow 500 EFLH. 7

8 Altrnativly this option can b usd for divrsity arrangmnts of vapour comprssion and Cognration absorption chillrs, whr th latr is usd for th pak loads only. - Doubl stag dirct fird chillrs: Th TEWI valus ar ovr 50% highr than thos of cntrifugal chillrs for most applications, i.. EFLH highr than 500 hours. At 125 EFLH it dos intrsct th cntrifugal TEWI lin. Dspit th nvironmntal disadvantags in crtain instancs this option has provd to b conomically viabl (Tozr 1994). Howvr, this option cannot b rcommndd on a TEWI basis unlss th EFLH ar blow 100 hours as in a divrsity arrangmnt of vapour comprssion and absorption chillrs A1,w85 TEWI tn CO2/lif A1,w100 A1,w115 A2,df A2,st A2,hr 1000 Cntrif EFLH Figur 1: TEWI of Absorption Chillrs 6. TEWI Calculations for Multistag Dirct Fird Absorption Chillrs Du to th outstanding high valus of TEWI for th dirct fird doubl stag absorption chillrs, a sris of spculativ calculations wr carrid out in ordr to prdict th bnfits to th nvironmnt of th dirct fird, tripl and quadrupl stag absorption chillrs. Th following Tabl 4 summariss th basic thortical and practical fficincy paramtrs. STAGES Thrmodynamic ratio α Burnr Efficincy ηburn Hat Dissipation Ratio HDR Tmpratur of Gnrator tg 150 C 190 C 230 COP Tabl 4: Paramtrs of Absorption Multistag Chillrs 8

9 For thortical cycls th thrmodynamic ratio α is dfind as th ratio of absolut vaporator and absorbr tmpraturs, and also dfins th idal COP for singl and multistag absorption cycls, whr N is th numbr of stags (Tozr 1992). T Tc α [14] Ta Tg 2 3 N COP α + α + α + + α [15] In this instanc it was assumd that th practical thrmodynamic ratio would incras as irrvrsibilitis within th cycls ar rmovd. Howvr, thy ar still at a rasonabl distanc from th idal valu of approximatly 0.9. Basd on th abov th TEWI calculations wr carrid out in a similar mannr to that dscribd prviously and th rsults ar indicatd in Figur TEWI tn CO2/lif A2,df A3,df A4,df Cntrif EFLH Figur 2: TEWI of Multistag Dirct Fird Absorption Chillrs From th figur it can b sn that only th four stag dirct fird absorption chillr can compt on a TEWI basis with cntrifugal chillrs. Thr stag chillrs, lik doubl stag chillrs can only b rcommndd for low EFLH applications, such as for short pak loads. Th assumptions ar that th ratio of Carbon Dioxid missions of gas combustion and of lctricity production rmain th sam, although thy will both improv with tim. If ths rsults ar compard with thos of othr authors (Oak Ridg Laboratory 1996), it can b sn that th rsults ar similar, although this papr indicats lowr TEWI valus for dirct fird absorption chillrs. Th rason for this is likly to b du to th lowr UK national lctric production fficincy. 9

10 7. Conclusions A Total Equivalnt Warming Impact (TEWI) analysis has bn carrid out on th ntir rang of singl and doubl stag absorption chillrs to dtrmin th most bnficial options. Ths includd th dirct fird absorption chillrs and th indirct drivn absorption chillrs from cognration systms. Ths wr basd on xrgy allocatd valus. Th bst slctions wr found to b doubl stag stam drivn absorption chillrs for all applications. Th nxt bst options ar singl stag hot watr drivn absorption chillrs for short running hour applications and divrsification whr th absorption chillrs ar usd only for th pak loads. Within th sam contxt doubl stag dirct fird absorption chillrs wr found to b fasibl for a vry narrow and limitd band of applications. Thrfor a spculativ calculation was carrid out for multistag dirct fird absorption chillrs. This provd that, basd on currnt tchnology, only th quadrupl stag dirct fird absorption chillr could compt on a TEWI basis with cntrifugal chillrs for a wid rang of oprating hours. A clar indication on th absorption systm divrsification influnc on TEWI has bn providd togthr with guidlins to mak this influnc positiv to th nvironmnt. Ths calculations ar basd on annual avrag CO2 missions rlatd to th lctricity gnration. Furthr work is rquird to ascrtain th impact of daily or sasonal variations which hav th potntial to influnc rsults significantly. A positiv impact to th nvironmnt is mainly achivd by avoiding dirct fird absorption chillrs and using indirct drivn absorption chillrs usd within intgratd nrgy systms such as cognration. Rfrncs Bggs C., 1994, Ic Thrmal Storag: Impact on Unitd Kingdom Carbon Dioxid Emissions, Building Srvics Enginring Rsarch & Tchnology, vol. 15(1), pp British Rfrigration Association, 1996, Guidlin mthods of calculating TEWI. Kotas T., 1995, Th xrgy mthod of thrmal plant analysis, Krigr Publishing Co., Malabar, Florida, ISBN Lozano M.A. and Valro A., 1993, Thory of th xrgtic cost, Enrgy Vol. 18, No 9, pp Lozano M.A., Valro A., Srra L. and Torrs C., 1994, Application of th xrgtic cost thory to th CGAM problm, Enrgy Vol. 19, No 3, pp Moran M., 1989, Availability analysis, a guid to fficint nrgy us, ASME Prss, ISBN

11 Oak Ridg National Laboratory, 28 Jun 1996, AFEAS Ovrsight Committ Lttr on TEWI Calculations Tozr R.M., 1991, Absorption Rfrigration, Larg Scal Dirct Fird Chillrs, MSc Thsis, IoEE, South Bank Univrsity, London. Tozr R.M., Oct. 1992, Absorption Rfrigration (principls, cycls and applications to cognration), Cognration 92, Madrid. Tozr R., Oct. 1994, Oprating comparison of absorption and cntrifugal chillrs, ASHRAE Journal, pp Tozr R., Nov. 1995, Cold Gnration Systms with Absorption Cycls, PhD Thsis, South Bank Univrsity, London. Tozr R. and Jams R., 1995, Absorption chillrs applid to Cognration systms, CIBSE, Building Srvics Rsarch & Tchnology, Vol. 16, No 4. Tozr R.M., Jams R.W. and Miguz C., Aug. 1995, Absorption cooling with Cognration, CIAR III, Ibro-Amrican Conf. of Air Cond. & Rfrig., Sao Paulo, Brazil, vol.2, pp Tozr R. and Jams R., 1996, Lif Cycl Costing of Absorption chillrs, CIBSE, Building Srvics Rsarch & Tchnology, in prss. Ur Z., 1995, Effctiv Control, Enrgy Efficincy and Systm Divrsification Influnc on TEWI, 19th Congrss of IIR, Th Hagu, Th Nthrlands. Ur Z., 1996a, Minimum TEWI through Intgratd Srvics", Rfrigration & Air Conditioning Burau, REVIEW, Issu 11, pp. 4. Ur Z., May 1996b, Intgratd air conditioning and food rfrigration is th right option for suprmarkts, ACR Today Journal, pp Appndix A: Introduction to Exrgy Q T0 m1 h1 T m2 h2 s1 W s2 Figur A1: Thrmodynamic systm in a stationary stat 11

12 Considr a systm that works in a stationary stat (Lozano & Valro 1993). Th balancs of mass, nrgy and ntropy ar: m1 m2 m [A1] W mh ( 2 h1 ) Q [A2] Q φ s ms ( 2 s1) 0 [A3] T whr φ s is th gnratd ntropy du to intrnal irrvrsibilitis. Not: φ s 0 implis a rvrsibl procss φ s > 0 implis a irrvrsibl procss Givn T 0 as th ambint tmpratur, and combining th nrgy quation [A2] with th ntropy quation [A3], and oprating as [A2]-T 0 [A3]: T0 W m[ ( h2 T0s2) ( h1 T0s1) ] Q 1 + T0φ s T [A4] This quation provids th xrgy balanc of th systm and all th quation trms hav xrgy units. Th following trms ar idntifid, whr th final trm is zro for a rvrsibl procss mh ( T 0 s) xrgy of flow T0 Q 1 xrgy of hat T T 0 φ s xrgy dstruction By analysing th xrgy of hat th Carnot factor is drivd, which is th ratio of thrmal xrgy to thrmal nrgy: T0 fcarnot 1 T [A5] To produc a chang from stat 1 to 2 on th mass flow in a systm that only xchangs hat with th ambint (T T 0 ), a minimum amount of work will b rquird. It will b qual to th diffrnc of xrgy of flow btwn stats 2 and 1 which is qual to m h T s h T s, whn th procss is intrnally rvrsibl ( φ ). [( ) ( )] T s Anothr point of intrst in rfrigration is to considr Q as th cooling capacity of a room at tmpratur T. Th hat dissipatd to th outdoor nvironmnt at T 0, is Q 0. Th rfrigration plant works a cycl in a closd systm. Applying th xrgy quation [A4] to this systm: T0 T0 W Q0 1 Q 1 + T0φ s [A6] T T 0 T0 W Q 1 + T s T 0φ [A7] From quation [A7] it can b sn that th minimum amount of work rquird for rfrigration is QT ( 0 T) T which corrsponds to th Carnot rvrsibl cycl, whr mor work will b rquird for coldr rooms, in addition to th xtra work du to irrvrsibilitis (T 0 φ s ). Appndix B: TEWI Allocations to Cognration lctrical and thrmal nrgy 12

13 Unlss othrwis spcifid th nrgy cost allocation considrs that th spcific xrgy costs of both thrmal and lctric nrgis ar idntical. Th sam assumption is mad with rgard to allocating TEWI valus to thrmal and lctric nrgy. FUEL i: natural gas 120 C F 500 C GAS ENGINE WORK or ELECTRIC ENERGY W THERMAL EXERGY B Hot Watr 106 / 90 C Figur B1: TEWI Allocation Schmatic Th xrgtic fficincy is th ratio of product and ful xrgis, which can b xprssd in trms of th work producd and th quality of thrmal nrgy producd. T0 P W + B W + Q f W + Q( 1 ) η b carnot T F F F F [B1] Also b b b η η + η η + η [B2] w q w q f carnot Th invrs of th xrgtic fficincy (η) is th spcific xrgy consumption (k), th ratio of th xrgy of th thrmal and lctric products (P) with rspct to th xrgy of th natural gas ful (F). F k 1 [B3] P η b Th spcific xrgtic cost (k*) considrs th ful cost: k* cngk [B4] Thrfor th lctricity and thrmal xrgy costs supplid by th cognration plant ar both qual to th spcific xrgtic cost (k*): b b cw cq k* [B5] By using th sam concpt to allocat TEWI valus: b b CO2w CO2q [B6] b η To xprss ths costs in trms of nrgy valus, th lctric xrgy will rmain unchangd bcaus in this cas nrgy is qual to xrgy. In th cas of thrmal nrgy, th magnitud of nrgy will b th Carnot factor tims largr than th thrmal xrgy, and thrfor its TEWI valu will b rducd by th sam ratio: 13

14 CO2w [B7] b η fcarnot CO2q [B8] b η If a crtain amount of th hat producd by th cognration plant is dumpd, this will hav an incrasing ffct on th thrmal and lctric nrgy costs. For this purpos th utilisation factor has bn dfind to vary btwn 0 and 1: ε q 0 if all th hat is dumpd ε q 1 if all th hat is utilisd (no hat dumpd) Th xrgtic fficincy is rducd by introducing th utilisation factor: b b b η ηw + ηq ηw + εqηq f carnot [B9] Th rduction of xrgtic fficincy incrass th TEWI valus which ar thrfor: CO2w [B10] ηw+ εqηqf carnot fcarnot CO2q [B11] ηw+ εqηqf carnot If all th hat is dumpd th following quation rsults which clarly producs highr TEWI valus than quation [B10] whn no hat is dumpd. CO2w [B12] η Exampl w Givn a gas ngin cognration plant with th following dtails: Elctric nrgy fficincy η w 03. Thrmal nrgy fficincy η q 045. Thrmal nrgy tmpraturs: 90 C to 105 C Full thrmal nrgy utilisation ε q 1 Rfrnc tmpratur t 0 28 C CO2 missions of natural gas CO20.18 kg CO2/kWh natural gas T f 0 carnot T ( )/ 2 Thrfor th TEWI of lctric nrgy is: CO2w ηw+ εqηqf carnot CO2w ηw+ εqηqf carnot 018. CO2 w kg CO2 / kwh Th TEWI of thrmal nrgy is: CO2 CO2 f kg CO2 / kwh q w carnot Whn ths valus ar compard to thos of natural gas (0.18) and th lctric grid (0.53), th TEWI advantags of Cognration bcom obvious. 14